Question

what is the length of chord \\(\overline{cd}\\) in \\(\odot o\\) below?

a. 8.02 units
b. 16.04 units
c. 4.01 units
d. 8.31 units

Explanation:

Identify equidistant chords

$$ d(O, AB) = 8.31 $$

$$ d(O, CD) = 8.31 $$

$$ d(O, AB) = d(O, CD) \implies AB = CD $$

Determine the length of chord AB

$$ \text{Perpendicular from center bisects the chord} \implies AB = 2 \times 8.02 = 16.04 $$

Calculate the length of chord CD

$$ CD = AB = 16.04 $$

Answer:

• (A) 8.02 units
• (B) 16.04 units (Correct answer)
• (C) 4.01 units
• (D) 8.31 units